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Free spells gained when going up a level must be Common spells taken from the Core Rulebook. Non core classes (such as a Witch or Inquisitor) whose spells lists aren't in the core rulebook, treat any spells in their original spell lists as Common.
Other spells must be purchased (or obtained via 'adventuring') before they can be learnt. The cost of these spells is higher than normal due to their rarity.
|Other Paizo Source||Rare||x5||+10|
|Non-Paizo Source||Very Rare||x10||+15|
This doesn't mean that all such spells are available (especially for non-Paizo sources).
Common spells automatically gained when going up a level are gained immediately after a night's rest. It is assumed that you've been studying prior to that.
Wizards and other book learners can learn other spells by spending time studying and researching them. If you have a copy of the spell, it takes 1 full day per spell level, and success is automatic.
If you don't have a copy of the spell, then you need to research the spell. It takes 1 week per spell level, and the cost is 100gp per level of the spell in materials. You need to make a Spellcraft check equal to 10 + 3 x level of the spell, modified by rarity. If you fail, you lose the money and the time. You can try again, and get a cumulative +1 for each previous attempt at that spell.
As for Arcane spells, Divine spells can only be selected from the Core Rulebook unless the character has had a chance to study them first. Temples, NPCs or scrolls are possible sources. Temples and NPCs will generally charge for access to these spells.
Once studied, such a spell can be selected normally.
Costs are as for Arcane spells.
If you are a Psychic character (not permitted by default), then spells in Occult Mysteries, as well as any spells on your basic class list, can be used as your free spells when starting and levelling up. Otherwise they count as Uncommon, though a PC Psychic will probably have a source they can go to.
There is a restriction on how good some items can be. Weapons and armour are limited by their type, so bigger weapons and heavier armour are easier to enchant than smaller of lighter items.
Weapons are limited by the maximum damage they do. A weapon can have a maximum enhancement bonus equal to half it's maximum damage (round down), to a limit of +5. This is the base damage of the weapon. So a dagger (d4) is limited to +2, a longsword (d8) to +4. A small dagger (d3) is limited to +1.
Armour is limited to half the armour bonus (rounded up), to a maximum of +5.